Problem: The grades on a physics midterm at Santa Rita are normally distributed with $\mu = 67$ and $\sigma = 2.0$. Luis earned a $72$ on the exam. Find the z-score for Luis's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Luis's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{72 - {67}}{{2.0}}} $ ${ z \approx 2.50}$ The z-score is $2.50$. In other words, Luis's score was $2.50$ standard deviations above the mean.